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离散GM(1,1)模型与灰色预测模型建模机理 被引量:249

Discrete GM(1,1) and Mechanism of Grey Forecasting Model
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摘要 GM(1,1)模型中,从离散形式到白化形式的转变,以及GM(1,1)模型预测稳定性问题,一直困扰着灰色系统理论的研究者.本文以此为研究出发点,从由离散到离散的角度解决这一理论问题,建立了离散灰色预测模型(称DGM(1,1)模型),并对其与原GM(1,1)模型的关系做了深入研究,找出了原模型预测不稳定的原因,利用麦克劳林公式展开对这些原因做全面解释,最后用纯指数序列验证DGM(1,1)模型预测的无偏性,研究结果表明,可以将本文建立的DGM(1,1)模型作为灰色预测模型的精确形式,而原模型作为近似形式加以使用. In grey forecasting model, there are two unsolved problem, the theoretical basis of transformation from discrete form to continuous form and the forecasting stability, which puzzled those who are absorbed in grey theory. Many scholars used all kinds of methods to revise the model, and they have made some progress, but they didn't solve it absolutely in principle. To solve these two problem and on the basis of the angle from discrete to discrete, discrete grey forecasting model(which is called DGM(1,1)) is constructed. And the relationship between it and original grey forecasting model is studied on, also the course of unstability in original grey forecasting model is found out. And it is explained by using DGM(1,1). Finally a series of accurative index number is used to prove the unbiased property of DGM(1,1). It is indicated that the simulative result is satisfied and DGM(1,1) can be considered as the precise form of grey forecasting model and original GM(1,1) as approximate form.
作者 谢乃明 刘思峰 XIE Nai-ming, LIU Si-feng(College of Economic&Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)
出处 《系统工程理论与实践》 EI CSCD 北大核心 2005年第1期93-99,共7页 Systems Engineering—Theory & Practice
基金 国家自然科学基金,高等学校博士学科点专项科研项目,江苏省自然科学基金,南京航空航天大学校科研和教改项目
关键词 灰色模型 离散 稳定性 预测 白化 grey model discrete stability forecast whitenization
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